We could say that in The West Wing world there was an issue with Nixon resigning. Maybe Ford was never named VP and instead of following the line to the presidency (which is really screwed up by the 25th Amendment) that they instead had a special election.

Nothing in the constitution authorizes a special election to fill the vacancy, including the 25th Amendment.

I suppose that it is possible that the 25th Amendment in the "Bartlettverse" provides for a special election, which would put the time divergence at approximately 1967, when that amendment was ratified.